PART 1. Simplification Using Boolean Algebra
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1 Name EET 1131 Lab #5 Logic Simplification Techniques OBJECTIVES: Upon completing this lab, you ll be able to: 1) Obtain the experimental truth table of a logic circuit. 2) Use Boolean algebra to simplify a logic circuit. 3) Use Karnaugh maps to simplify a logic circuit. 4) Verify that a logic circuit and its simplified version give the same output. 5) Use Multisim software to obtain a circuit s truth table and simplified expression. EQUIPMENT REQUIRED: Safety glasses ICs: 7408, 7432, and other chips as needed ETS-7000 Digital-Analog Training System Quartus II software and Altera DE2-115 board Multisim simulation software PART 1. Simplification Using Boolean Algebra PROCEDURE: 1. Consider the schematic diagram shown below. 2. In Quartus II, create a new project named Lab5Circuit1. Following the steps you learned in the previous lab, create a block diagram/schematic file that implements the circuit shown above. Then compile your design, assign input and output pin numbers so that you can use three switches as your inputs and an LED for your output, and download your design to the FPGA on the DE2-115 board. EET 1131 Lab #5 - Page 1 Revised 12/29/2014
2 3. Obtain and write the circuit s experimental truth table, using a straight edge to draw the lines in your truth table. 4. When your truth table is complete, ask me to check your work. Circuit works correctly? 5. From the schematic diagram (repeated below), write the Boolean expression for X as a function of A, B, and C. Do not simplify the expression using any of our rules or theorems just write the expression that you get directly from the diagram. X = EET 1131 Lab #5 - Page 2 Revised 12/29/2014
3 6. Now simplify this expression using the laws, rules, and theorems of Boolean algebra. Show each step in the simplification, and label each step with the rule, law, or theorem that you used in that step. When you re finished, ask me to check your simplified expression. EET 1131 Lab #5 - Page 3 Revised 12/29/2014
4 7. Draw the schematic diagram for your simplified expression. Write chip numbers and pin numbers on it. 8. Build the simplified circuit on the breadboard. Obtain and write its experimental truth table, using a straight edge to draw the lines in your truth table. 9. When your truth table is complete, ask me to check your work. Safety glasses? Circuit works? DIPs inserted correctly? Using power/ground busses? Wire colors? Wire lengths? Wire ends trimmed? DIPs accessible? 10. How does your truth table in Step 9 compare to your truth table in Step 4? EET 1131 Lab #5 - Page 4 Revised 12/29/2014
5 PART 2. Simplification Using Karnaugh Maps PROCEDURE: 12. Consider the new schematic diagram shown below. 13. In Quartus II, create a new project named Lab5Circuit2. Create a block diagram/schematic file that implements the circuit shown above. Then compile your design, assign input and output pin numbers so that you can use four switches as your inputs and an LED for your output, and download your design to the FPGA on the DE2-115 board. 14. Test your circuit, and write the circuit s truth table on the next page. EET 1131 Lab #5 - Page 5 Revised 12/29/2014
6 15. Obtain and write the circuit s experimental truth table, using a straight edge to draw the lines in your truth table. Now write the SOP expression that you get directly from this truth table. Do not simplify. X = 16. Ask me to check your work. SOP expression correct? EET 1131 Lab #5 - Page 6 Revised 12/29/2014
7 17. From your SOP expression, use a straight edge to draw the circuit s Karnaugh map. Then read off the simplified expression from the K-map. Simplified expression: X = Call me over to check your K-map and simplified expression. 18. Draw the schematic diagram for this simplified expression. Label the gates with chip numbers and pin numbers. (You re free to use chips not listed on the front page of this lab.) EET 1131 Lab #5 - Page 7 Revised 12/29/2014
8 19. Build the simplified circuit on the breadboard. Obtain and write its experimental truth table. 20. When your truth table is complete, ask me to check your work. Safety glasses? Circuit works? DIPs inserted correctly? Using power/ground busses? Wire colors? Wire lengths? Wire ends trimmed? DIPs accessible? 21. How does your truth table in Step 20 compare to your truth table in Step 16? EET 1131 Lab #5 - Page 8 Revised 12/29/2014
9 PART 3. Simplification Using Multisim 23. Shown below is the circuit from Part 1 of this lab. Draw this circuit in Multisim. Then connect Multisim s Logic Converter as shown below. Notice that you don t need to hook up V CC or ground to use the Logic Converter. 24. Double-click the Logic Converter to open it. Then press its button to generate a truth table. 25. How does the Logic Converter s truth table compare to your results from Step 4 and Step 9? 26. Press the Logic Converter s button to generate a simplified expression. 27. How does the Logic Converter s simplified expression compare to your simplified expression from Step 7? 28. Copy and paste your circuit diagram and the Logic Converter into a Microsoft Word document, so that they both fit on a single page. Make sure that you can read the Logic Converter s truth table and simplified expression. Print this page out and turn it in with your lab. EET 1131 Lab #5 - Page 9 Revised 12/29/2014
10 29. Shown below is the circuit from Part 2 of this lab. Draw this circuit in Multisim. (If you can t find a 7411 in Multisim, you can use a 74LS11 or AND3.) Then use Multisim s Logic Converter to obtain the circuit s truth table and simplified expression. 30. Copy and paste your schematic diagram and the Logic Converter into a Microsoft Word document, so that they both fit on a single page. Make sure that you can read the Logic Converter s complete truth table and simplified expression. Print this page out and turn it in with your lab. 31. How do the results of Step 31 compare to results from earlier steps in Part 2 of this lab? EET 1131 Lab #5 - Page 10 Revised 12/29/2014
11 32. Write chip numbers and pin numbers on each gate in the drawing below. (This is a new circuit, completely different from the circuits that you ve been working with on the previous pages.) 33. From the diagram, write the Boolean expression for Y as a function of A, B, and C. Do not simplify the expression using any of our rules or theorems just write the expression that you get directly from the diagram. Y = 34. Draw the circuit in Multisim. Connect Multisim s Logic Converter, and use it to generate the circuit s truth table. Copy this truth table below. 35. Use the Logic Converter to find the simplified expression for this circuit. Note that Multisim uses apostrophes instead of overbars to show that a variable is complemented. For example, the complement of A is written in Multisim as A instead of A. Copy the simplified expression below, but use overbars instead of apostrophes. Y = 36. Copy and paste your schematic diagram and the Logic Converter into a Microsoft Word document, so that they both fit on a single page. Make sure that you can read the Logic Converter s truth table and simplified expression. Print this page out and turn it in with your lab. EET 1131 Lab #5 - Page 11 Revised 12/29/2014
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